Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1038 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 1038 conjugacy classes of subgroups — too many to draw. Only its 179 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #10595992 | C2 | semidirect |
| 3. #10592838 | C2 | semidirect |
| 4. #10592830 | C2 | semidirect |
| 5. #10592705 | C2 | semidirect |
| 6. C32×#344 | C2 | semidirect |
| 7. #10589423 | C2 | semidirect |
| 18. C2×#3745 | C4 | semidirect |
| 19. C2×#3744 | C4 | semidirect |
| 31. C3×#344 | D3 | semidirect |
| 44. C2×C4⋊(C3⋊D3) | C2×C4 | semidirect |
| 49. C2×#634 | C2×C4 | semidirect |
| 55. C2×C32×C8 | C2×C4 | semidirect |
| 122. #344 | C3⋊D3 | semidirect |
| 146. C2×C3×C8 | C4×D3 | semidirect |
| 255. C2×C8 | C4×C3⋊D3 | semidirect |
| 284. C32 | #1904 | semidirect |
| 340. C3 | #69027 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64117 | 2 |
| #10595992 | 2 |
| #10592838 | 2 |
| #10592830 | 2 |
| #10592705 | 2 |
| C32×#344 | 2 |
| #10589423 | 2 |
| #69027 | 3 |